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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Continuous maps of the interval with finite nonwandering set
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by Louis Block PDF
Trans. Amer. Math. Soc. 240 (1978), 221-230 Request permission

Abstract:

Let f be a continuous map of a closed interval into itself, and let $\Omega (f)$ denote the nonwandering set of f. It is shown that if $\Omega (f)$ is finite, then $\Omega (f)$ is the set of periodic points of f. Also, an example is given of a continuous map g, of a compact, connected, metrizable, one-dimensional space, for which $\Omega (g)$ consists of exactly two points, one of which is not periodic.
References
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 240 (1978), 221-230
  • MSC: Primary 54H20; Secondary 58F20
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0474240-2
  • MathSciNet review: 0474240